If something is stable, it is not likely to change or come to an end suddenly.

If someone has a stable personality, they are calm and reasonable and their mood does not change suddenly.

You can describe someone who is seriously ill as stable when their condition has stopped getting worse.

Chemical substances are described as stable when they tend to remain in the same chemical or atomic state.

If an object is stable, it is firmly fixed in position and is not likely to move or fall.

A stable or stables is a building in which horses are kept.

A stable or stables is an organization that breeds and trains horses for racing.